Hacer Şengül Kandemir

• Associate Professor
• Harran University

In the paper, neutrosophic statistical analysis of temperature data of different cities in the southeastern Anatolia region of Turkey is given. The neutrosophic mean and neutrosophic coefficient of variation are computed using the temperature data. From the analysis, it is concluded that the temperatures of Mardin and Şanlıurfa cities are more cons...

In this study, the concepts of lacunary [Formula: see text]summability of order [Formula: see text], lacunary strongly harmonic summability of order [Formula: see text], lacunary statistical logarithmic convergence of order [Formula: see text] of sequences of real numbers are introduced and relations between these concepts are investigated.

We investigate the concept of \(\rho\)-strongly summable and \(\rho\)-statistical convergence for double sequences of order \(\alpha\) in topological groups by using definition of \(\rho\)-statistical convergence which was defined by Cakalli in Bulletin of the Malaysian Mathematical Sciences Society 40:1701–1710 . We give some inclusion relations b...

In this paper, we introduce the concept of strongly lacunary convergence of order ? of difference sequences of fractional order in the neutrosophic normed spaces. We investigate a few fundamental properties of this new concept.

The main object of this article is to introduce the concepts of (f, ρ)− statistical convergence of order α and strong (f, ρ)− summability of order α of sequences of real numbers and give some inclusion relations between these spaces.

In this study, by using definition of ρ-statistical convergence which was defined by Çakallı [5], we introduce the concepts of pointwise wρα(f)-summability, pointwise ρ-statistical convergence of order α and uniform ρ-statistical convergence of order α sequences of real-valued functions. Also, we give some inclusion relations between these concepts...

In this paper, we introduce strong $N_{\alpha }^{\beta }(\theta ,A,F)-$convergence and $S_{\alpha }^{\beta }(\theta ,A,F)-$% convergence with respect to a sequence of modulus functions and give some connections between strongly $N_{\alpha }^{\beta }(\theta ,A,F)-$convergent sequences and $S_{\alpha }^{\beta }(\theta ,A,F)-$convergent sequences for...

The idea of statistical convergence was given by Zygmund [45] in the first edition of his monograph published in Warsaw in 1935 and then was considered as a summability method by Schoenberg [38] in 1959 despite the fact that it made its initial appearance in a short note by Fast [16] and Steinhaus [42] in 1951. Along with the theory of summability...

In this paper, we introduce the concept of strongly \lambdaλ-convergence of order \alphaα in the neutrosophic normed spaces. We investigate some fundamental properties of this new concept.

The main object of this article is to introduce the concepts of (f, ρ)- statistical convergence of order α and strong (f, ρ)- summability of order α of sequences of real numbers and give some inclusion relations between these spaces.

In this study, by using definition of ρ-statistical convergence which defined by Çakallı [5] we introduce the concepts of pointwise -summability, pointwise ρ-statistical convergence of order α and uniform ρ-statistical convergence of order α sequences of real-valued functions. Also, we give some inclusion relations between these concepts.

In this study, by using definition of rho-statistical convergence which was defined by Cakalli [5], we give some inclusion relations between the sets of rho-statistical convergence and statistical convergence in topological groups.

In this study, the concepts of lacunary (H, 1) summability of order α, lacunary strongly harmonically summability of order α, lacunary statistical logarithmic convergence of order α of sequences of real numbers are introduced and relations between these concepts are investigated. 2015 Mathematics Subject Classification: 40A05, 40C05, 46A45

In this paper, we introduce the concepts of ideal ∆α−lacunary statis- tical convergence of order β with the fractional order of α and ideal ∆α−lacunary strongly convergence of order β with the fractional order of α ( where 0 < β ≤ 1and α be a fractional order) and give some relations about these concepts.

In this article, we introduce and investigate the concepts of Δ θ m ‐asymptotically statistical equivalent of order α ˜ and strong Δ θ m ‐asymptotically equivalent of order α ˜ of double sequences. Also, we give some relationships related to these concepts.

In this paper, we introduce the concepts of Δα-deferred statistical convergence with the fractional order of α and Δα- strongly convergence with the fractional order of α. Additionally, we give some relations about these concepts.

In this study, we introduce and examine the concepts of Δm−weighted statistical convergence and Δm−weighted (N¯,pn)−summability. Also some relations between Δm−weighted statistical convergence and Δm−weighted (N¯,pn)−summability are given.

In this paper, we introduce the concept of strong ρ−convergence of order β ( or Npβ (ρ) −convergence ) of sequence of real numbers and give some inclusion relations between the set of all ρ−statistical convergence of order β and strong Npβ (ρ)− convergence.

In this study, by using definition of ρ-statistical convergence which was defined by Ç akallı[2], we give some inclusion relations between the set of ρ-statistical convergence and strong (S, [ρ]) summability.

The main purpose of this paper is to introduce the concepts of Wijsman deferred statistical convergence of order α and Wijsman strong deferred Cesàro convergence of order α for sequences of sets.

The main purpose of this work is to introduce and examine the concept of (λ,f)-statistical boundedness of order α and give the relations between some known concepts and (λ,f)-statistical boundedness of order α.

In this paper we introduce the concepts of strongly deferred Cesàro summable and \(\mu \)-deferred statistical convergence of real-valued functions \(x=x(t)\) which are measurable (in the Lebesgue sense) in the interval \([1,\infty )\). In addition, the relations between the set of strong deferred Cesàro summable and \(\mu \)-deferred statistical c...

The main object of this article is to introduce the concepts of f-lacunary statistical convergence of order alpha and strong f-lacunary summability of order alpha of double sequences and give some inclusion relations between these concepts.

In this paper, the concepts of deferred statistical convergence of order α and deferred strong Cesàro summability are generalized to general metric spaces and some relations between deferred strong Cesàro summability of order α and deferred statistical convergence of order α are given in general metric spaces.

A sequence (αk) of points in ℝ, the set of real numbers, is called ρ-statistically convergent of order β to an element ℓ of ℝ if limn→∞ℓρnβ|{k≤n:|αk−ℓ|≥ε}|=0 for each ε > 0 and 0 < β ≤ 1, where ρ = (ρn) is a non-decreasing sequence of positive real numbers tending to ∞ such that lim supnρnβn<∞, Δρnβ=O(1), and Δαn = αn+1 − αn for each positive inte...

In this study, using a lacunary sequence we introduce the concepts of lacunary d−statistically convergent sequences and lacunary d−statistically bounded sequences in general metric spaces.

In this paper, the concept of deferred statistical convergence of order α is generalized to topological groups, and some inclusion relations between the set of all statistically convergent sequences of order α in topological groups and the set of all deferred statistically convergent sequences of order α in topological groups are given.

The main purpose of this paper is to introduce and investigate the concepts of deferred strong summability and deferred statistical convergence of real-valued functions which are measurable (in the Lebesgue sense) in the interval (1, ∞). Some relations between deferred strong summability and deferred statistical convergence of real-valued functions...

In this paper, the definitions of lacunary strong A−convergence of order (α, β) with respect to a modulus and lacunary A–statistical convergence of order (α, β) are given. We study some connections between lacunary strong A-convergence of order (α, β) with respect to a modulus and lacunary A-statistical convergence of order (α, β).

The main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of order (alpha,beta) of sequences of real numbers. Strongly ideal lacunary ward continuity of order (alpha,beta) is also investigated. Interesting results are obtained.

In this paper we introduce the concepts of Wijsman $% \left( f,I\right) -$lacunary statistical{\Large \ }convergence of order $% \alpha $ and Wijsman strongly $\left( f,I\right) -$lacunary statistical% {\Large \ }convergence of order $\alpha ,$ and investigated between their relationship.

The main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of order (α, β) of sequences of real numbers. Strongly ideal lacunary ward continuity of order (α, β) is also investigated. Interesting results are obtained.

The idea of I−convergence of real sequences was introduced by Kostyrko et al. [Kostyrko, P., Šalát, T. and Wilczyński, W. I−convergence, Real Anal. Exchange 26(2) (2000/2001), 669-686] and also independently by Nuray and Ruckle [Nuray, F. and Ruckle, W. H. Generalized statistical convergence and convergence free spaces. J. Math. Anal. Appl. 245(2)...

In this study, we introduce the concepts of pointwise deferred statistical convergence and strongly deferred Cesàro pointwise summable sequences of fuzzy mappings. Some relations between pointwise deferred statistical convergence and strongly deferred Cesàro pointwise summable sequences of fuzzy mappings are given.

In this paper we introduce the concepts of Wijsman (f, I) −lacunary statistical convergence of order α and Wijsman strongly (f, I) −lacunary statistical convergence of order α, and investigated between their relationship.

In this paper, the definitions of lacunary strong A−convergence of order α with respect to a modulus and lacunary A−statistical convergence of order α were given by adding α to the definitions of lacunary strong A−convergence with respect to a modulus and lacunary A−statistical convergence when A = (aik) is an infinite matrix of complex numbers and...

In the paper [37], we introduce the concepts of f-lacunary statistical convergence of order (alpha,beta) and strong f-lacunary summability of order (alpha,beta) of sequences of real numbers for 0 <alpha<=beta<= 1, where f is an unbounded modulus and give some inclusion relations between these concepts. In this paper we continue to examine others re...

In this study we introduce and examine the concepts of ?m-asymptotic deferred statistical equivalence of order ? and strong ?mr-asymptotic deferred equivalence of order ? of sequences of real numbers. Also, we give some relations connected to these concepts.

The idea of I-convergence of real sequences was introduced by Kostyrko et al. [Kostyrko, P., Sal?t, T. and Wilczy?ski, W. I-convergence, Real Anal. Exchange 26(2) (2000/2001), 669-686] and also independently by Nuray and Ruckle [Nuray, F. and Ruckle,W. H. Generalized statistical convergence and convergence free spaces. J. Math. Anal. Appl. 245(2) (...

The main object of this article is to introduce the concepts of f −lacunary statistical convergence of order α and strong f−lacunary summability of order α of sequences of real numbers and give some inclusion relations between these spaces.

The notion of the α th order Δ i m - lacunary statistical convergence and α th order lacunary strongly (Δ i m , p)-summable sequences was introduced by Altınok et al. [1]. They also gave significant inclusion correlation associated with the aforementioned sequence spces. In this paper, our aim is to exploit some other important relations between th...

The main purpose of this paper is to introduce the concept of strongly ideal lacunary quasi-Cauchyness of sequences of real numbers. Strongly ideal lacunary ward continuity is also investigated. Interesting results are obtained.

The idea of asymptotically equivalent sequences and asymptotic regular matrices was introduced by Marouf [ Marouf, M. Asymptotic equiva- lence and summability, Int. J. Math. Sci. 16(4) 755-762 (1993) ] and Patterson [ Patterson, RF. On asymptotically statistically equivalent sequences, Demonstr. Math. 36(1), 149-153 (2003) ] extended these concepts...

In this paper, we introduce the concepts of pointwise (λ, I)-statistical convergence of order α and pointwise wp(λ, I)-summability of order α. Also some relations between pointwise (λ, I)-statistical convergence of order α and pointwise wp(λ, I)-summability of order α are given.

The main purpose of this paper is to introduce the concepts of f–lacunary statistical convergence of order (α, β) and strong f–lacunary summability of order (α, β) of sequences of real numbers for 0 <α ≤ β ≤ 1, where f is an unbounded modulus.

The idea of I−convergence of real sequences was introduced by Kostyrko et al. [ Kostyrko, P.; Šalát, T. and Wilczyński, W. I−convergence, Real Anal. Exchange 26(2) (2000/2001), 669-686 ] and also independently by Nuray and Ruckle [ Nuray, F. and Ruckle, W. H. Generalized statistical convergence and convergence free spaces, J. Math. Anal. Appl. 245(...

In this paper, we define the generalized Cesàro difference sequence space C(p) (∆m) and consider it equipped with the Luxemburg normunder which it is a Banach space and we show that in the space C(p) (∆m) every weakly convergent sequence on the unit sphere converges is the norm, where p = (pn) is a bounded sequence of positive real numbers with pn...

In this paper, the concept of lacunary statistical convergence of order (α, β) is generalized to topological groups, and some inclusion relations between the set of all statistically convergent sequences of order (α, β) and the set of all lacunary statistically convergent sequences of order (α, β) are given.

In the present paper, we introduce a concept of ideal lacunary statistical quasi-Cauchy sequence of order α of real numbers in the sense that a sequence (x k ) of points in R is called I−lacunary statistically quasi-Cauchy of order α, if for each ε > 0 and for each δ > 0, where an ideal I is a family of subsets of positive integers N which is close...

In this study, we introduce and examine the concepts of Δ θ m −asymptotically statistical equivalent of order α and strong Δ θ m −asymptotically equivalent of order α of sequences. Also, we give some relations connected to these concepts.

In this paper we introduce the concepts of pointwise lacunary statistical convergence of order α and pointwise \(w_{p}(f,\theta )\) —summability of order α of sequences of real valued functions. Also some relations between pointwise \(S_{\theta }^{\alpha }(f)\) —statistical convergence and pointwise \(w_{p}^{\alpha }(f,\theta )\) —summability are g...

In this article, we introduce the concept of lacunary statistical convergence of order α of real number sequences and give some inclusion relations between the sets of lacunary statistical convergence of order α and strong Nθα(p)-summability. Furthermore, some relations between the spaces Nθα Sθα are examined.

In the paper [32], we have defined the concepts of lacunary statistical convergence of order ff and strong N-theta(p)-summability of order ff for sequences of complex (or real) numbers. In this paper we continue to examine others relations between lacunary statistical convergence of order alpha and strong N-theta(p)-summability of order alpha.